In this paper, we introduce several various classes of c-almost periodic type functions and their Stepanov generalizations, where c ∈ ℂ and |c| = 1. We also consider the corresponding classes of c-almost periodic type functions depending on two variables and prove several related composition principles. Plenty of illustrative examples and applications are presented.

The paper deals with a new algebra of generalized functions. This algebra contains Bochner almost automorphic functions and almost automorphic distributions. Properties of this algebra are studied.

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The aim of this paper is to introduce and to study an algebra of almost periodic generalized functions containing the classical Bohr almost periodic functions as well as almost periodic Schwartz distributions.

The main aim of this paper is to indicate that the notion of semi- c -periodicity is equivalent with the notion of c -periodicity, provided that c is a nonzero complex number whose absolute value is not equal to 1.

In this paper, we introduce the classes of $(\omega, c)$-pseudo almost periodicfunctions and $(\omega, c)$-pseudo almost automorphicfunctions. These collections include $(\omega, c)$-pseudo periodicfunctions, pseudo almost periodic functions and their automorphic analogues.We present an application to the abstract semilinear first-order Cauchy inclusions in Banach spaces.

The paper is a study of the (w, c) −pseudo almost periodicity in the setting of Sobolev-Schwartz distributions. We introduce the space of (w, c) −pseudo almost periodic distributions and give their principal properties. Some results about the existence of distributional (w, c) −pseudo almost periodic solutions of linear differential systems are proposed.